Electronic structure, reflectivity and X-ray luminescence of MAPbCl3 crystal in orthorhombic phase

Band structure calculations and reflectivity spectra

Below 172 K, MAPbCl₃ adopts a distorted perovskite structure with orthorhombic space group (Pnma)³² where the PbCl₆ octahedra are tilted relative to the ideal perovskite geometry (see Fig. 1 right).

Left – photo of single crystal of MAPbCl₃ with size 7 × 7 × 2 mm³. Right – the crystal structure of the orthorhombic phase (Pnma group) of MAPbCl₃ where MA is methylammonium (CH₃NH₃).

The arrangement of molecular ordering pattern induces a permanent structural distortion of the PbCl₆ octahedra at low temperatures, resulting in an antiferroelectric striped pattern in the crystallographic a-direction³³. Therefore, when modelling the crystal, we specifically chose this direction to be aligned with the MA molecules. Table 1 presents the calculated lattice parameters and lattice volume of unit cell for the orthorhombic phase of MAPbCl₃.

The calculated results demonstrate strong agreement with the experimental data. This agreement was achieved by employing the PBEsol parametrization of the GGA, which was specifically developed to enhance the description of exchange interactions in solids. PBEsol provides improved structural parameters and total energy predictions for solids, addressing the limitations of the standard PBE, which tends to overestimate lattice parameters³⁴. It is important to acknowledge that while PBEsol enhances the accuracy of conventional GGA functionals, previous studies have shown that hybrid functionals such as HSE06 or self-interaction corrected methods often provide a more reliable description of electronic properties, particularly in bandgap predictions^35,36. Nevertheless, while PBEsol tends to underestimate the absolute value of the bandgap, this does not impact the further analysis of the results and still ensures an accurate reproduction of the energy band positions.

Next, we calculated the band energy diagram which provides detailed insight into the electronic structure of MAPbCl₃. The band energy diagrams for the orthorhombic crystal phase of the crystal are plotted along the high-symmetry points of the first Brillouin zone: Г→Z→T→Y→S→X→U→R, with the Fermi level set at 0 eV corresponding to the top of the valence band (VB).

The band energy structure obtained using GGA-PBEsol functionals without (a) and with (b) Spin-orbit coupling (SOC) for orthorhombic MAPbCl₃. The Fermi level indicates a dashed line at 0 eV. A and B mark the excitonic transitions observed in reflectivity.

The band energy diagrams for the low-temperature orthorhombic phase of MAPbCl₃ perovskite reveal that both the top of the valence band (VB) and the bottom of the conduction band (CB) are located at the Γ point (see Fig. 2a), confirming the formation of a direct band gap. The calculations yielded a band gap of 2.52 eV, which is 0.6 eV lower than the experimentally measured value³⁸. To more accurately capture the influence of the heavy Pb atom on the electronic structure of MAPbCl₃, additional calculations were performed with the inclusion of the spin-orbit coupling (SOC) effect. Incorporating SOC significantly alters the band dispersions, which is crucial for interpreting the material optoelectronic properties³⁹. The inclusion of SOC results in a narrowed band gap of 1.33 eV (Fig. 2b). This underestimation of the band gap is a known feature of SOC-inclusive calculations, as SOC induces a pronounced splitting of the CB in Pb-based perovskites⁴⁰. The calculated band gap values, both with and without SOC, are consistent with previous theoretical estimates for the low-temperature phase of MAPbCl₃, which reported gaps of 2.3 eV and 1.2 eV, respectively^41,42. Despite the inherent limitations of DFT ground-state calculations, particularly their tendency to underestimate certain properties such as bandgap values, the derived conclusions about energy band dispersions and their symmetries remain robust. These results offer a reliable basis for construction of accurate semi-empirical Hamiltonians, especially in scenarios demanding precise descriptions of Bloch states and selection rules.

The nature of the valence band (VB) top and conduction band (CB) bottom in MAPbCl₃ can be elucidated through first-principles calculations using density functional theory (DFT). The density of states (DOS) and projected density of states (PDOS) were computed over the energy range from − 14 to 9 eV, which can be broadly divided into three distinct regions corresponding to the bands shown in Fig. 3. The first region, spanning approximately from − 14 eV to −3 eV, corresponds to deep states within the VB. The second region, from − 3 eV to 0.4 eV, includes states that significantly contribute to the VB near the Fermi level. The third region, ranging from 2.9 eV to 6.8 eV, represents the upper portion of the CB. These calculations provide detailed insight into the electronic structure of MAPbCl₃, highlighting the specific energy contributions to the VB and CB, and helping to understand the optoelectronic properties. As follow from these results most of chlorine s-states form deep energy levels around − 14 eV and have minimal impact on the conduction band (CB) or valence band (VB). Within the energy range of −11 to −3.5 eV, clusters of energetic s- and p-states from the methylammonium cation are observed, alongside hybridized s-states from lead. In MAPbCl₃, the upper valence band is primarily composed of halide p orbitals, with minor anti-bonding contributions from Pb 6s² orbitals, while the conduction band is dominated by Pb 6p orbitals^41,43,44,45. Although the molecular cation MA does not directly contribute to the electronic band edges⁴², it influences the crystal structure and indirectly affects the band gap.

The DOS and PDOS calculated using GGA-PBEsol functional for orthorhombic MAPbCl₃.

MAPbCl₃ is a direct band gap semiconductor exhibiting in high symmetry cubic phase the global extremum at the R point of the BZ and a secondary extremum at the M point. Modelling suggests the possibility of optically allowed transitions at both the R and M points, a phenomenon referred to as multiband gap absorption⁴⁶. It is pertinent to remark that the electronic structure of the low-temperature orthorhombic phase has its origin in the cubic phase structure⁴⁷; therefore in further discussion the notations of critical points from the highest symmetry phase are used for consistency. The strong spin-orbit coupling characteristic of materials containing heavy lead atoms leads to the formation of split states within the conduction band, further influencing the electronic properties of the material.

It should be noted that the calculations do not account for electron-hole interactions and, therefore, cannot capture exciton effects, manifested as sharp peaks in different regions of the absorption and reflection spectra of the crystal. This limitation has significant implications for the photo physics of perovskites, as exciton effects are crucial for enabling efficient light emission and the generation of electron-hole pairs across a broader range of excitation energies^48,49. Despite this limitation, the calculated band structure of MAPbCl₃ still provides valuable insights, allowing for the assignment of key features observed in the crystal reflectivity spectrum, as shown in Fig. 4. The reflectivity spectrum exhibits a clear excitonic transition, labelled as peak A, at 3.22 eV. This is followed by a second sharp peak, marked as B, at 3.94 eV, with subsequent peaks C, D, and E appearing at 4.44, 4.66, and 5.36 eV, respectively.

Reflectivity spectra of MAPbCl₃ at 10 K. The spectra in VUV (black) and UV (blue) range are shown separately as they are measured using different experimental setups.

The position of the peak A aligns with recent reports for MAPbCl₃⁵⁰. The excitonic character of the first sharp peak, observed at 3.22 eV in the reflectivity spectra of APbCl₃ crystals, has been well-established and recognized for some time^51,52,53. The excitonic nature of the first peak in the reflection spectra has also been confirmed for other metal-halide counterparts MAPbX₃ with X = Br, I^50,54. Interestingly, optical spectra measurements beyond the first peak are more common for inorganic perovskites^{51,52,53,55,56,57,58,59,60}, in contrast to MAPbX₃. Existing data primarily come from spectroscopic ellipsometry studies of thin films^44,45. Thus, it is sensible to analyse the reflectivity of MAPbCl₃ using as a guidance prior data on the reflectivity of CsPbCl₃. Following this approach, the sharp peak B at 3.94 eV can be attributed to the optically allowed second exciton transition at the M point of BZ. Observation of such transition is consistent with the concept of multiband structure of metal-halide perovskite crystals discussed in⁴⁶. The subsequent peaks, labelled C and D, are associated with transitions from the uppermost valence band to the upper regions of the conduction band at the R and M points, respectively. Peak E is likely due to transitions from the lower part of the valence band to various parts of the conduction band, influenced by the spin-orbit splitting of the Pb 6p states. Transitions involving the MA cation begin above 6 eV, resulting in band F. As photon energy increases, the involvement of additional states in the transitions increases, which can lead to a smearing of spectral features. This complexity introduces certain level of ambiguity in the interpretation of the reflectivity spectra in this higher energy range.

X-ray luminescence spectra with temperature

Previous studies of X-ray luminescence in MAPbCl₃ crystals have shown significant thermal quenching, with peak intensity decreasing by two orders of magnitude when the temperature exceeds 150 K^22,61. The X-ray luminescence spectra for the MAPbCl₃ crystal measured in this work exhibit a similar pattern as illustrated in Fig. 5. At 15 K, the crystal shows distinct emission peaks at 389 nm (1), 392 nm (2), and 404 nm (3), along with a broad shoulder at 418 nm (4). Additionally, a weaker broad emission band is observed at 470 nm (5), extending from 440 to 550 nm.

As temperature increases, the spectra undergo notable changes: peaks 1 and 2 merge into a single band with a maximum at 391 nm. Peak 3 gradually shifts to 400 nm, while shoulder 4 and the broad band emission 5 disappear as the temperature rises above 70 K. With further temperature increase, the amplitudes of the remaining peaks at 391 and 400 nm continue to decrease due to thermal quenching. At 100 K, the luminescence intensity of MAPbCl₃ is reduced by an order of magnitude compared to the value at 15 K.

X-ray luminescence spectra of a MAPbCl₃ crystal measured at different temperatures.

There is relatively large body of published results on the luminescence properties of organic-inorganic perovskites which are commonly used for interpretation and assignment of the main features observed in the X-ray luminescence spectra. This, however, requires caution because of a strong near-edge absorption and excitation density effects that can cause significant shape alteration of the observed spectra. Specifically absorption can cause red shift in the emission peaks⁶² while variation of excitation density can lead to changes in the intensity distribution of these peaks^28,29. To rationalise the interpretation of X-ray spectra, we measured the luminescence spectrum of MAPbCl₃ at photoexcitation at 350 nm. The X-ray and photoluminescence spectra recorded at T = 15 K are compared in Fig. 6.

In direct semiconductors the highest energy sharp peak in the luminescence spectra is typically associated with the radiative decay of free excitons⁴⁸. This assignment is also commonly applied to the first peak observed at 387 nm (denoted as peak 1′) in the photoluminescence spectra of MAPbCl₃^22,24,38,50. Due to the short penetration depth of photons of 350 nm (< 10^− 8 m), the emission from free excitons originates from the thin surface layer of the crystal.

In contrast, X-ray excitation creates the electronic excitations within a much thicker layer of the crystal, on the order of 10^− 4–10^− 3 m, depending on the energy of X-rays⁶³. This difference in excitation depth leads to a redshift in the emission of free excitons from the bulk of the crystal. Therefore, with a relatively high degree of certainty, the peak at 389 nm (peak 1) observed in the X-ray luminescence spectra can be attributed to the radiative decay of free excitons, consistent with findings from previous studies²². Nonetheless, it is worth mentioning a less likely, yet still possible, explanation for the observed spectral changes—structural modifications in the excited states induced by high-energy X-rays.

Luminescence spectra of a MAPbCl₃ crystal measured at excitation with X-rays and photons 350 nm (T = 15 K). The assignments of specific peaks marked by numbers is provided in the text.

The sharp peaks between 390 and 430 nm, labelled 2′, 3′, 3′′, 4, and 4′′ in the photoluminescence spectra of MAPbCl₃ crystals at low temperatures, are frequently reported in literature^24,38,50,64. These peaks are believed to have an excitonic origin and are attributed to the radiative decay of excitons bound to traps and defects. Therefore, it is reasonable to extend this interpretation to the corresponding peaks 2, 3, and 4 observed in our X-ray luminescence spectra. It should be noted that due to the lower spectral resolution of our experimental setup, the structure of peaks 3 and 4 in the X-ray luminescence spectra remains unresolved. The broad low-energy band 5 observed in our X-ray luminescence spectra at 470 nm is tentatively attributed to the defect-related emission, similar to emission observed in other metal-organic halide perovskites^22,50,65. The emission in this spectral range exhibits decay time (~ 10^− 6 s) which is supporting the proposed assignment. The trapping may occur at halide vacancies, which are the predominant deep defects in the MAPbCl₃ crystal predicted by theory⁶⁶.

Luminescence decay at X-ray excitation

To get further insight into the dynamic of emission processes in the crystal under study we investigated the kinetics of luminescence decay under pulsed X-ray excitation from a synchrotron source. The changes of the measured decay curves of MAPbCl₃ crystals with temperature are displayed in Fig. 7. These decay curves, recorded in integral mode (capturing photons across the entire luminescence spectrum of the crystal), reveal complex kinetics resulting from various recombination processes and emission centres. Initially, the decay curves exhibit a rapid decrease in intensity following the excitation pulse. To accurately characterize the decay processes, the measured curves were subjected to deconvolution analysis⁶⁷. This analysis allowed us to isolate and recover the intrinsic luminescence decay characteristics by accounting for the known instrumental response function (IRF).

Following the deconvolution the decay curves were fitted using the sum of two exponentials:\(f\left( t \right)={A_1}{\text{exp}}\left( { – t/{\tau _1}} \right)+{A_2}{\text{exp}}\left( { – t/{\tau _2}} \right)+{y_0}\) where \({A_{1,2}}\) and \({\tau _{1,2}}\) are the amplitudes and decay time constants of the two emission components, \({y_0}\) is a constant background. At very low temperatures, a single exponential function plus background was sufficient to fit the data. However, at temperatures above 20 K, a second exponential component was necessary to account for the slower decay process. The temperature-dependent decay time constants and amplitudes obtained from the fits are presented in Fig. 8.

Decay curves of X-ray luminescence measured in the MAPbCl₃ crystal at different temperatures. The luminescence is excited by X-ray pulses of synchrotron radiation at energy 14 keV.

Temperature dependence of decay constants (top) and amplitudes with background (bottom) obtained from the fitting of the decay curves of MAPbCl₃ by a sum of two exponential functions.

The initial phase of the luminescence decay is characterized by a sub-nanosecond component with a decay time of approximately 0.2 ns at 10 K. This extremely rapid decay is indicative of excitonic processes occurring on a similar timescale, a feature that has been observed in other halide perovskites^{25,28,54,68,69}. At elevated temperatures, a delayed decay component with a time constant of around 1 ns becomes evident. This longer-lived component is likely due to the radiative recombination of bound excitons released from shallow traps^69,70. A very slow emission component with a decay time exceeding 10^− 7 s, associated with the radiative recombination of electrons and holes from deeper traps, is not distinguishable in the measured decay curves at these timescale as it primarily contributes to the background. It is notable that the amplitudes of both decay components initially increase with temperature, suggesting that these recombination channels are enhanced by thermally stimulated processes. Specifically, the exciton channels are likely to be fed by the thermally induced release of trapped excitons, as indicated by the decrease in the amplitude of the background component with rising temperature. This behaviour is consistent with previous observations in MAPbI₃ crystals, where changes in luminescence kinetics with temperature were attributed to the exchange of particles between different radiative decay channels²¹.